This demonstrates how a Maclaurin Expansion can approximate a function very well, even quite far from zero, if enough terms are included

[list=1][br][*]How many terms would be necessary for the function of the Maclaurin Expansion to be a good approximation to [math]sin x[/math] when [math]x[/math] is:[br][list=a][br][*]0.5[br][*]-1[br][*]-2[br][*]-4[br][*]-8[br][/list][br][*]The Maclaurin Expansion is not a good way to approximate [math]sin[/math]-100. Why not?[br][/list]